Coalescing Cellular Automata

Jean-Baptiste Rouquier 1 Michel Morvan 1
1 LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both configurations become identical after a reasonable time. We prove coalescence for two elementary rules and show that there exists infinitely many coalescing CA. We then conduct an experimental study on all elementary CA and show that some rules exhibit a phase transition, which belongs to the universality class of directed percolation.
keyword : cellular automata directed percolation asynchronous cellular automata phase transition
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Submitted on : Wednesday, October 4, 2006 - 3:36:27 PM
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Jean-Baptiste Rouquier, Michel Morvan. Coalescing Cellular Automata. International Conference on Computational Science (ICCS 2006) : Advancing Science through Computation. Workshop "Modelling of Complex Systems by Cellular Automata" (MCSCA 2006), University of Reading, United Kingdom, May 2006, Reading, United Kingdom. pp.321-328, ⟨10.1007/11758532_44⟩. ⟨ensl-00103510⟩

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